Stabilisation of linear delay difference inclusions via time-varying control Lyapunov functions

The stabilisation of linear delay difference inclusions is often complicated by computational issues and the presence of constraints. In this study, to solve this problem, a receding horizon control scheme is proposed based on the Razumikhin approach and time-varying control Lyapunov functions. By allowing the control Lyapunov function to be time varying, the computational advantages of the Razumikhin approach can be exploited and at the same time the conservatism associated with this approach is avoided. Thus, a control scheme is obtained which takes constraints into account and requires solving on-line a low-dimensional semi-definite programming problem. The effectiveness of the proposed results is illustrated via an example that also shows the computational limitations of existing control strategies